Is the Jim Henson Company involved at all in the new movie?

Yes, as it turns out, The Jim Henson Company was indeed somewhat involved with the film;
According to the film's credits (I also found it on Muppet Wiki) the costumes were provided by Jim Henson's Creature Shop.

And of course, the fact that the movie was partly filmed at The Jim Henson Company lot. Filming there obviously required their cooperation.

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Between that and the use of Henson studios for the Muppet Studios, Id say thats a pretty good involvement